Given a circle with center $O$ and a point $P$ not lying on it, let $X$ be an arbitrary point on this circle and $Y$ be a common point of the bisector of angle $POX$ and the perpendicular bisector to segment $PX$. Find the locus of points $Y$.
Problem
Source: Sharygin Geometry Olympiad 2014 - Problem 6
Tags: geometry, perpendicular bisector, geometry unsolved